I know that exponential decay can be done by so... $a\exp(-x/b)$ where $b$ is the factor that determines how quickly the values will decay and $x$ is the input. My question is how can I apply this to a range of data so that the decay is evenly distributed regardless of how many values are in the range?
Let's say for example I have a data range of $10$ values, $1$-$10$. How can I modify the equation so when I have $20$ values, $1$-$20$, that the output is proportional to the size of the data. Ie. $f(2)$ for $10$ values = $f(4)$ $20$ values, $f(6)$ for $20$ values = $f(18)$ $60$ values, etc.
Apologies if this is something simple.